In this article, an approximate analytical solution of an
integro-differential system of equations is constructed, which describes
the process of intense boiling of a superheated liquid. The kinetic and
balance equations for the bubble-size distribution function and liquid
temperature are solved analytically using the Laplace transform and
saddle-point methods with allowance for an arbitrary dependence of the
bubble growth rate on temperature. The rate of bubble appearance
therewith is considered in accordance with the Dering-Volmer and
Frenkel-Zeldovich-Kagan nucleation theories. It is shown that the
initial distribution function decreases with increasing the
dimensionless size of bubbles and shifts to their greater values with
time.